虎门体育官方登录入口网

报告题目: Weak metric regularity of the KKT mapping in nonsmooth optimization   

报 告 人: 郑喜印 教授

报告时间: 2026年 9月 18 日（星期五）15:45-16:30    

地   点：1号楼1306

邀 请 人: 潘少华教授

欢迎广大师生前往！

数学虎门体育app下载官网

2026年9月14日

报告摘要：

Considering that the metric regularity and Aubin property in optimization theory are often too restrictive in applications, this paper introduces and studies the weak metric regularity and weak Aubin property. For optimization problem $\mathcal{P}_A(f)$ with a nonsmooth objective function $f$ and a closed constraint set $A$, it is proved that the weak Aubin property of the solution mapping $x^*\mapsto{\rm argmin}_{x\in A}f_{x^*}(x):=f(x)-\langle x^*,x\rangle$ of the tilt perturbed problems $\mathcal{P}_A(f_{x^*})$ implies its single valuedness and that the weak Aubin property of the solution mapping of canonically perturbed conic optimization problems also implies its single valuedness and continuity. In the convex case, it is proved that the KKT mapping $x\mapsto\partial f(x)+N(A,x)$ of $\mathcal{P}_A(f)$ is weakly metrically regular if and only if the solution mapping $x^*\mapsto{\rm argmin}_{x\in A}f_{x^*}(x)$ of its tilt-perturbed problems is single-valued and continuous if and only if tilt-perturbed problems $\mathcal{P}_A(f_{x^*})$ are uniformly well-posed solvable with respect to $x^*$ on some neighborhood of 0. Under the usual metric regularity of the KKT mapping, some sharper results are obtained.

报告人简介：

郑喜。愀壑形拇笱Р┦，云南大学教授， 博士生导师， 长期从事变分分析和非光滑优化理论的交叉研究，发表学术论文百余篇，其中30余篇发表在数学优化权威刊物 “SIAM J. Optim.”、 “Math. Program.”和 “Math. Oper.Math.”， 作为第一完成人获二项云南省自然科学奖一等奖。